There is ample evidence that masking and social distancing are effective in reducing severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission. However, due to the complexity of airborne disease transmission, it is difficult to quantify their effectiveness, especially in the case of one-to-one exposure. Here, we introduce the concept of an upper bound for one-to-one exposure to infectious human respiratory particles and apply it to SARS-CoV-2. To calculate exposure and infection risk, we use a comprehensive database on respiratory particle size distribution; exhalation flow physics; leakage from face masks of various types and fits measured on human subjects; consideration of ambient particle shrinkage due to evaporation; and rehydration, inhalability, and deposition in the susceptible airways. We find, for a typical SARS-CoV-2 viral load and infectious dose, that social distancing alone, even at 3.0 m between two speaking individuals, leads to an upper bound of 90% for risk of infection after a few minutes. If only the susceptible wears a face mask with infectious speaking at a distance of 1.5 m, the upper bound drops very significantly; that is, with a surgical mask, the upper bound reaches 90% after 30 min, and, with an FFP2 mask, it remains at about 20% even after 1 h. When both wear a surgical mask, while the infectious is speaking, the very conservative upper bound remains below 30% after 1 h, but, when both wear a well-fitting FFP2 mask, it is 0.4%. We conclude that wearing appropriate masks in the community provides excellent protection for others and oneself, and makes social distancing less important.

Introduction Many countries with an early outbreak of SARS-CoV-2 struggled to gauge the size and start date of the epidemic mainly due to limited testing capacities and a large proportion of undetected asymptomatic and mild infections. Iran was among the first countries with a major outbreak outside China. Methods We constructed a globally representative sample of 802 genomes, including 46 samples from patients inside or with a travel history to Iran. We then performed a phylogenetic analysis to identify clades related to samples from Iran and estimated the start of the epidemic and early doubling times in cases. We leveraged air travel data from 36 exported cases of COVID-19 to estimate the point-prevalence and the basic reproductive number across the country. We also analysed the province-level all-cause mortality data during winter and spring 2020 to estimate under-reporting of COVID-19-related deaths. Finally, we use this information in an SEIR model to reconstruct the early outbreak dynamics and assess the effectiveness of intervention measures in Iran. Results By identifying the most basal clade that contained genomes from Iran, our phylogenetic analysis showed that the age of the root is placed on 2019-12-21 (95 % HPD: 2019-09-07 – 2020-02-14). This date coincides with our estimated epidemic start date on 2019-12-25 (95 %CI: 2019-12-11 – 2020-02-24) based air travel data from exported cases with an early doubling time of 4.0 (95 %CI: 1.4–6.7) days in cases. Our analysis of all-cause mortality showed 21.9 (95 % CI: 16.7–27.2) thousand excess deaths by the end of summer. Our model forecasted the second epidemic peak and suggested that by 2020-08-31 a total of 15.0 (95 %CI: 4.9–25.0) million individuals recovered from the disease across the country. Conclusion These findings have profound implications for assessing the stage of the epidemic in Iran despite significant levels of under-reporting. Moreover, the results shed light on the dynamics of SARS-CoV-2 transmissions in Iran and central Asia. They also suggest that in the absence of border screening, there is a high risk of introduction from travellers from areas with active outbreaks. Finally, they show both that well-informed epidemic models are able to forecast episodes of resurgence following a relaxation of interventions, and that NPIs are key to controlling ongoing epidemics.

We measure the deformation of particles made of several slender arms in a two-dimensional (2D) linear shear and a three-dimensional (3D) turbulent flow. We show how these measurements of arm deformations along with the rotation rate of the particle allow us to extract the velocity gradient tensor of the flow. The particles used in the experiments have three symmetric arms in a plane (triads) and are fabricated using 3D printing of a flexible polymeric material. Deformation measurements of a particle free to rotate about a fixed axis in a 2D simple shear flow are used to validate our model relating particle deformations to the fluid strain. We then examine deformable particles in a 3D turbulent flow created by a jet array in a vertical water tunnel. Particle orientations and deformations are measured with high precision using four high speed cameras and have an uncertainty on the order of 10 −4 radians. Measured deformations in 3D turbulence are small and only slightly larger than our orientation measurement uncertainty. Simulation results for triads in turbulence show deformations similar to the experimental observations. Deformable particles offer a promising method for measuring the full local velocity gradient tensor from measurements of a single particle where traditionally a high concentration of tracer particles would be required.

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We examine the spatial field of orientations of slender fibers that are advected by a two-dimensional fluid flow. The orientation field of these passive directors are important in a wide range of industrial and geophysical flows. We introduce emergent scar lines as the dominant coherent structures in the orientation field of passive directors in chaotic flows. Previous work has identified the existence of scar lines where the orientation rotates by {\pi} over short distances, but the lines that were identified disappeared as time progressed. As a result, earlier work focused on topological singularities in the orientation field which we find to play a negligible role at long times. We use the standard map as a simple time-periodic two-dimensional (2D) flow that produces Lagrangian chaos. This class of flows produce persistent patterns in passive scalar advection, and we find that a different kind of persistent pattern develops in the passive director orientation field. We identify the mechanism by which emergent scar lines grow to dominate these patterns at long times in complex flows. Emergent scar lines form where the recent stretching of the fluid element is perpendicular to earlier stretching. Thus these scar lines can be labeled by their age, defined as the time since their stretching reached a maximum.Comment: 12 Pages, 12 Figure